Common, complex diseases like cancer, heart disease and type 2 diabetes are multifactorial: risk for these diseases depends on multiple genetic and environmental factors. To date, however, epidemiological studies searching for genetic markers associated with disease risk have considered the effect of a single genetic factor, averaged over all other factors. If the effect of a genetic variant differs across strata defined by environmental exposures, then it is possible that the marginal approach will fail to detect the variant. In some situations, considering possible genetic effect modification by measured exposures can increase researchers' ability to detect genetic markers of disease. Most of the proposed methods for improving power to detect causal loci by considering gene-environment interaction focus on a single locus and a single environmental exposure. When more than one exposure might modify with a genetic effect, these methods force investigators either to guess a priori which exposure is the most likely modifier or to test individual exposures in series, leading to an increase in multiple testing penalty and a loss of power. We propose two analytic frameworks that flexibly model the interactions between a genetic marker and multiple measured exposures. We hypothesize that these approaches will be more powerful than tests that focus on a single exposure, or consider multiple exposures individually, in series. Successful completion of our aims will provide researchers with tools to improve their ability to identify genetic variants associated with complex human traits, which will in turn lead to a better understanding of the multifactorial mechanisms underlying human disease and potential improvements in risk prediction and prevention programs.